What is 13-(8-5 2/3 \times 2/1) ?

The solution to 13-(8-5 2/3 \times 2/1) is 16 1/3

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13-(8-5 2/3 \times 2/1)

Solution

13 - (8 - 5 \frac{2}{3} \cdot \frac{2}{1})

Solution

16 \frac{1}{3}

Solution steps

13 - (8 - 5 \frac{2}{3} \cdot \frac{2}{1})

Convert mixed numbers to improper fractions:

5 \frac{2}{3} = \frac{17}{3}

5 \frac{2}{3}

Convert mixed numbers to improper fraction:

a \frac{b}{c} = \frac{a \cdot c + b}{c}

5 \frac{2}{3} = \frac{5 \cdot 3 + 2}{3}

= \frac{17}{3}

= 13 - (8 - \frac{17}{3} \cdot \frac{2}{1})

\frac{2}{1} = 2

Apply rule

\frac{a}{1} = a

2

= 13 - (8 - \frac{17}{3} \cdot 2)

Follow the PEMDAS order of operations

Calculate within parentheses

(8 - \frac{17}{3} 2) : - \frac{10}{3}

8 - \frac{17}{3} \cdot 2

8 - \frac{17}{3} \cdot 2 = - \frac{10}{3}

8 - \frac{17}{3} \cdot 2

\frac{17}{3} \cdot 2 = \frac{34}{3}

\frac{17}{3} \cdot 2

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{17 \cdot 2}{3}

Multiply the numbers:

17 \cdot 2 = 34

= \frac{34}{3}

= 8 - \frac{34}{3}

Convert element to fraction:

8 = \frac{8 \cdot 3}{3}

= \frac{8 \cdot 3}{3} - \frac{34}{3}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{8 \cdot 3 - 34}{3}

8 \cdot 3 - 34 = - 10

8 \cdot 3 - 34

Multiply the numbers:

8 \cdot 3 = 24

= 24 - 34

Subtract the numbers:

24 - 34 = - 10

= - 10

= \frac{- 10}{3}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{10}{3}

= - \frac{10}{3}

= 13 - (- \frac{10}{3})

Add and subtract (left to right)

13 - (- \frac{10}{3}) : \frac{49}{3}

13 - (- \frac{10}{3})

Apply rule

- (- a) = + a

- (- \frac{10}{3}) = + \frac{10}{3}

= 13 + \frac{10}{3}

13 + \frac{10}{3} = \frac{49}{3}

13 + \frac{10}{3}

Convert element to fraction:

13 = \frac{13 \cdot 3}{3}

= \frac{13 \cdot 3}{3} + \frac{10}{3}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{13 \cdot 3 + 10}{3}

13 \cdot 3 + 10 = 49

13 \cdot 3 + 10

Multiply the numbers:

13 \cdot 3 = 39

= 39 + 10

Add the numbers:

39 + 10 = 49

= 49

= \frac{49}{3}

= \frac{49}{3}

= \frac{49}{3}

Convert improper fractions to mixed numbers:

\frac{49}{3} = 16 \frac{1}{3}

\frac{49}{3} = 16

Remainder

1

\frac{49}{3}

Write the problem in long division format

3 \overline{∣ 49}

Divide

4

3

to get

1

Divide

4

3

to get

1

1 3 \overline{∣ 49}

Multiply the quotient digit

(1)

by the divisor

3

1 3 \overline{∣ 49} \underline{3}

Subtract

3

from

4

1 3 \overline{∣ 49} \underline{3} 1

Bring down the next number of the dividend

1 3 \overline{∣ 49} \underline{3} 19

1 3 \overline{∣ 49} \underline{3} 19

Divide

19

3

to get

6

Divide

19

3

to get

6

16 3 \overline{∣ 49} \underline{3} 19

Multiply the quotient digit

(6)

by the divisor

3

16 3 \overline{∣ 49} \underline{3} 19 \underline{18}

Subtract

18

from

19

16 3 \overline{∣ 49} \underline{3} 19 \underline{18} 1

16 3 \overline{∣ 49} \underline{3} 19 \underline{18} 1

The solution for Long Division of

\frac{49}{3}

16

with remainder of

1

16 Remainder 1

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{49}{3} = 16 \frac{1}{3}

= 16 \frac{1}{3}

= 16 \frac{1}{3}

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1 1/3 \times 5\div 2/3

1 \frac{1}{3} \times 5 \div \frac{2}{3}

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(- 9) (- 6 + 4 - 7 - 2 + 8 - 3 + 9)

50-8\times 5\div 10

50 - 8 \times 5 \div 10

Frequently Asked Questions (FAQ)

What is 13-(8-5 2/3 \times 2/1) ?
The solution to 13-(8-5 2/3 \times 2/1) is 16 1/3